摘要
本文利用一种新方法对Fokker- Planck方程的非古典势对称群生成元进行研究,找到方程的几个非古典势对称群生成元,并采用非古典对称群方法由这些对称群生成元构造得到Fokker- Planck方程的相应显式解.这些新显式解不能由Fokker -Planck方程本身的Lie对称或Li-e B cklund对称来获得.在验证所求得显式解的过程中,还发现并得到了另外几个显式解.这些新显式解则不能由Fokker -Planck方程本身的Lie对称,Lie- B cklund对称或非古典势对称来获得.文章表明,通过偏微分方程的非古典势对称群生成元来寻找其显式解是可能的.
Nonclassical potential symmetries of Fokker-Planek equation are determined by using a new method,and some class of new explicit solutions, which can not be obtained through the Lie symmetries or Lie-Baeieklund symmetries of Fokker-Planck equation, are constructed by using nonclassical symmetry method to these new symmetry generators. In the process of verificatio derived from the Lie symmetries, Lie-Baecklund symmetries or n, N more explicit solutions, which can not be onclassical potential symmetries of Fokker- Planck equation,are found. It＇s shown that there is possibility of finding new explicit solutions of partial differential equations through their nonclassical potential symmetries.
出处
《动力学与控制学报》
2006年第2期103-108,共6页
Journal of Dynamics and Control
基金
国家自然科学基金资助项目(10272021
10572021)
高等学校博士学科点专项科研基金(20040007022)~~
